We present an application of an iterative deconvolution algorithm to speckle interferometric data. This blind deconvolution algorithm permits the recovery of the target distribution when the point spread function is either unknown or poorly known. The algorithm is applied to specklegrams of the multiple star systems, and the results for (zetz) UMa are compared to shift-and-add results for the same data. The linearity of the algorithm is demonstrated and the signal-to-noise ratio of the reconstruction is shown to grow as the square root of the number of specklegrams used. This algorithm does not require the use of an unresolved target for point spread function calibration.